Censored stable processes

• 成果类型: Article
• 署名作者: Bogdan, K; Burdzy, K; Chen, ZQ
• 署名单位: Wroclaw University of Science & Technology; University of Washington; University of Washington Seattle
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-003-0275-1
• 发表日期: 2003
• 页码: 89-152
• 关键词: boundary harnack principle; intrinsic ultracontractivity; harmonic-functions; conditional gauge; dirichlet forms; sobolev spaces; domains; DIFFUSIONS

摘要

We present several constructions of a censored stable process in an open set D subset of R, i.e., a symmetric stable process which is not allowed to jump outside D. We address the question of whether the process will approach the boundary of D in a finite time - we give sharp conditions for such approach in terms of the stability index alpha and the thickness of the boundary. As a corollary, new results are obtained concerning Besov spaces on non-smooth domains, including the critical exponent case. We also study the decay rate of the corresponding harmonic functions which vanish on a part of the boundary. We derive a boundary Harnack principle in C-1,C-1 open sets.